Three centuries ago, when sailing ships were essential to the military and economic might of nations, a key problem was to understand the wind patterns of Earth. Of particular importance were the Trade winds, named in recognition of their importance to intercontinental commerce. The easterly winds in this low latitude belt were well known to sailors to be persistent and reliable. George Hadley (1735) offered an explanation based on these observations and his remarkable intuition of how global atmospheric circulation would be influenced by Earth’s rotation and temperature variations. Hadley’s single-cell notion is shown in Fig. 1a with computed flow lines curved to account for the Coriolis force. Hot air will rise near the equator, where solar heating is greatest, replaced by cold air that descends at the poles, where insolation is least. A flat circulation system called a “Hadley Cell”, or unicell, develops, with flow just above the surface directed toward the equator, and high level winds being poleward. Earth’s rotation skews the surface winds in the easterly sense known to sailors, while the high elevation return flow is skewed in a westerly sense. This Coriolis effect arises from variations in the tangential speed of different latitudinal belts of the rotating Earth, and has opposite effects on air masses displaced toward or away from the equator.

Hadley had a great idea, but he had the wrong planet! The thick atmosphere of Venus appears to circulate in a single, gigantic Hadley cell (Fig. 1b). Earth’s circulation pattern is more complicated because it rotates much more rapidly- every 24 h compared to 243 days for Venus, and because of many secondary influences including the irregular distribution of ocean currents, continents and mountain ranges. On a grand scale, though, Earth’s rotation appears to have broken the two Hadley cells into several parallel cells, those nearest the equator still called “Hadley cells”. The “Ferrel cells” at middle N and S latitudes, and the “Polar cells” are found above Earth’s polar caps (Fig. 1c).

Global Belts

Figure 2 provides a remarkably realistic overview of the observed, first-order patterns of winds, pressure and precipitation over Earth’s surface. Distributed symmetrically about the equatorial “Intertropical Convergence Zone” (ITCZ) are the Trade wind belts, the Horse latitudes, the Westerlies, the Polar fronts, and the Polar caps, all zones known long ago to sailors and explorers.

Figure 2. Global belts that characterize atmospheric circulation.

The ITCZ is a zone near the equator that features calm winds, persistent low pressure, and high, yearlong precipitation. The intense solar insolation and resultant high temperature drives air to ascend, producing low surface pressure, high precipitation, and the cancellation of surface winds (return flows) from the north and south. This zone of global convergence comprises the ascending parts of the symmetrical Hadley cells to the immediate north and south (Fig. 2). Due to the vigor of this ascent, the Troposphere- the lower 9 to 14 km of the atmosphere that hosts practically all weather phenomena, is higher here than elsewhere on Earth.

Symmetrically located about the ITCZ are the parallel Trade wind belts, representing the converging limbs of Earth’s two Hadley cells (Fig. 2). Surface winds are easterly. The Trade belts extend to latitudes of 30 deg N and 30 S, corresponding to the Horse Latitudes, whose colorful name has debated origins. This zone is characterized by inconsistent winds, persistent high pressure, low humidity, low precipitation, and anomalously high temperature, and it hosts many of the great deserts of the world including the Sahara. Figure 2 provides an explanation for these features in that the descending limbs of the Hadley cell and the adjacent Ferrel cell occur here. In particular, air is warmed and its humidity lowered by adiabatic compression during this decent.

Next are the Westerlies, reliable winds also of great importance to sailors. In particular, for travel between the Old and New World, an outgoing voyage driven by Trade Winds could be coupled with a return trip that exploited the Westerlies. The historical significance of this couple to the colonization of the world cannot be overstated. Figure 2 explains these surface winds in terms of the Coriolis effect, their westerly direction deriving from their poleward component of motion.

The poleward terminus of the Westerlies lies near the two Polar fronts, which are zones of intense storms and unsettled weather. Figure 2 explains these active, persistent fronts as additional zones of global convergence and ascending air, somewhat similar to the ITCZ. There is one major difference, however. The Polar Fronts are the ascending boundaries between the Ferrel cells and the Polar cells, whose air masses have markedly different temperatures, and the result is intense weather (see below). In contrast, the two Hadley cells that converge near the ITCZ have similar temperatures, and while rainfall is high, the weather is not violent and Hurricanes are rare. Earth’s jet streams generally lie near the top of the Troposphere, above the Polar Fronts, and are undulating, quasi-stationary belts of extremely fast winds that commonly are 100 to 300 km/h.

Last are the cold air masses that reside over the polar caps. The poles themselves are zones of persistent high pressure and dry descending air, as suggested by the “Polar cells” of Fig. 2. Though it may come as a surprise, the polar caps are meteorological deserts, and have some of the lowest precipitation totals on Earth. For example, average precipitation at the South Pole is only about 4 cm of water equivalent per year, about the same as a hyperarid desert. This is due to the descending air as well as to the extremely low temperatures, because such cold air cannot hold appreciable water vapor (see below). Figure 2 should be committed to memory. Though clearly a simplification, it is easy to draw and it codifies many observed, first-order features of Earth’s atmosphere and climate.

Vertical Structure of the Atmosphere

This lower part of the atmosphere that is familiar to humans is called the troposphere. As discussed in detail below, the troposphere extends to heights of about 9 to 14 km, about where jets fly. This layer contains about ¾ of the mass of the entire atmosphere, and is the site of all ordinary weather phenomena.

However, Earth’s atmosphere extends to great heights of several hundred km that are much different in character than the familiar troposphere. Long before rockets we knew that the atmosphere continues to such heights, because bright meteors, aurorae, and other phenomena were observed and triangulated. Because the reduction of pressure with height is almost exponential (Fig. 3, blue line), the atmosphere becomes highly rarified above the troposphere.

It is well known that the air becomes cooler as one climbs a mountain or otherwise ascends in the troposphere, but continuation of that
rapid upward cooling is not possible. Using high altitude balloon flights, Teisserenc de Bort discovered that the troposphere is overlain by a distinct layer, which he termed the stratosphere, which lacks this progressive reduction of temperature. In fact, stratospheric temperatures actually increase with height, while pressure decreases to about 1/1000 of that at sea level as the top of this layer is approached, at an altitude of about 50 km (Fig. 3). The stratosphere contains the ozone layer, which shields Earth’s surface from dangerous UV radiation.

The overlying mesosphere, located between about 50 and 85 km, features progressive drops in both temperature and pressure (Fig. 3). Even though pressures are very low, enough air is present that meteors moving at astronomical speeds of 10-30 km/s become incandescently hot due to friction, so they can be seen.

The thermosphere extends from about 85 km to heights of several hundred kilometers, where the International Space Station orbits.

Temperatures again rise with altitude in the thermosphere, attaining great values, but pressure is so low that our ordinary concept of temperature has little meaning, and only its thermodynamic definition is relevant. Some of the gas is ionized, so the aurorae occur in this layer.

The chemical composition of the troposphere, stratosphere, mesosphere and lowermost thermosphere is generally uniform, so together this zone is sometimes called the homosphere, and the breathable gas mixture is called air. In contrast, above ~100 km the average molecular weight of atmospheric gas decreases with altitude. This heterosphere, which includes most of the thermosphere plus the overlying exosphere, represents Earth’s extended fringe zone where gas is slowly lost to space.

An important distinction is that the chemical uniformity of the homosphere does not apply to water and water vapor! These substances are strongly concentrated in the troposphere, and their effects greatly exceed what might be expected from their rather low abundances! The character of the troposphere is crucial to hydrologic science and is discussed in detail below.

Figure 3. Photograph of Earth’s atmosphere at sunset taken from the International Space Station about 350 km above the southern Ukraine showing atmospheric layers interpreted as indicated. The superimposed graph shows how temperature and pressure vary with height according to the 1976 US Standard Atmosphere model; this graph is scaled to approximately match the photo. (NASA photo ISS040-E-87351 taken 8/1/14).

Vertical Structure of the Lower Atmosphere

The lowermost layer of the atmosphere, called the Troposphere, hosts practically all phenomena that we recognize as weather. The troposphere is a zone of active convection that extends from Earth’s surface to heights of 9 to 14 km, being generally higher near the equator than at the poles. Jets fly near the top of this layer, exploiting jet stream winds whenever possible. Temperature at this level are roughly -40C, and pressure is low, about 300 millibar, so that nearly ¾ of the molecules in Earth’s atmosphere are below.

Because the troposphere is actively convecting, the air composition is very homogeneous. Normal dry air is about 78 wt. % nitrogen, 21% oxygen, 0.9 % argon, with tiny amounts of carbon dioxide (0.06%) and other gases. The amount of water vapor is low but variable, generally ranging from about 0.004 to 3.5%. The mean molecular weight of dry air is 28.97 g/mole.

The remarkably rapid, vertical rarefaction of the atmosphere is well known to mountain climbers, who on Earth’s highest peaks (8.8 km) require compressed air, yet commonly still suffer frostbite and other problems due to the cold, low oxygen conditions. This rarefaction is more remarkable when it is considered that Earth’s atmosphere extends to heights of about 150 km. Well known phenomena such as the aurora, meteor trails and fireballs typically occur in these high, extremely rarefied zones at 50 to 150 km above the surface.

The dependence of pressure (P) with height (z) can be determined from the hydrostatic equation, whose functional form can be reasoned because pressure is force/unit area:

where ρ is density and g the gravitational constant. In a compressible fluid such as air, the density depends on the pressure, as indicated by the ideal gas law,

where MW is the molecular weight and R the gas constant. These equations can be combined, then easily integrated if it assumed that g and T do not change too sharply with height. The well-known result is

where Ps is the surface pressure, and H is the “scale height”, representing the quantity RT/(g*MW), which is numerically equal to about 8.2 km for Earth’s lower atmosphere. This approximation explains the observed, rapid rarefaction of atmospheric pressure with height.to good accuracy.

Of course, balloonists have long known that air temperature becomes lower with height, at a rate of about 6.5 deg/km. Thus, as pressure is reduced with height, the air volume expands and the temperature drops. Because the troposphere is actively convecting, the thermodynamic condition approximates an adiabatic condition, represented by

where Cp is the isobaric heat capacity of the gas, and V the gas volume. This equation actually predicts that temperature should decrease at a rate of about 9.8 deg/km. This “dry adiabatic”, lapse rate is clearly much faster than the observed lapse rate. The reason stems from the small amount of water in the atmosphere, which condenses as ascending air is cooled, releasing the latent heat of vaporization along the way. Thus, temperatures aloft are not as cold as predicted by the dry air lapse rate, due to this extra heat. The thermodynamic condition for air saturated with water vapor is more difficult to calculate, but this “pseudoadiabatic” or “saturated adiabatic” lapse rate is known to be about 6.5 deg/km. The actual lapse rate in the lower atmosphere lies between the dry adiabat and saturated adiabatic rates, but is normally much closer to the latter. The bottom line is, the tiny amount of water vapor in Earth’s atmosphere has a great influence on Earth’s climate; the consequences are many and large.

Causes of Precipitation

Vapor Pressure of Water

The phenomenon of precipitations involves changes in the amount of H2O stored in the atmosphere. It is therefore important to know how much water vapor is present, and how temperature and pressure control that amount. The vapor pressures of numerous substances are known experimentally, and the results can be usefully calculated by the vant Hoff equation of thermodynamics. For the saturated vapor pressure (Psat, in torr) of liquid water at temperatures of 273 to 300K, the van’t Hoff equation can be approximated as:

where T is in Kelvins, as is always the case in thermodynamic relationships. Clearly, the vapor pressure increases exponentially. Similarly, the saturated vapor pressure above ice at subzero temperatures (<273.15k) is="" approximately:="">273.15k)>

To a very good approximation, Psat increases exponentially with temperature. However, the partial pressure (PH2O) of water in the actual atmosphere is normally below the saturated value. An important dimensionless ratio commonly reported by meteorologists is the relative humidity h, defined as

where Psat is calculated at the actual air temperature. Because both temperature and total pressure vary in real atmospheres, another important quantity is the “mixing ratio”, which normalized the content of water vapor in the atmosphere to its content of “dry air” (mostly N2, O2, and Ar). Thus,

The ratio of the molecular weights of water to dry air, 18.0/28.97, is conveniently close to the simple fraction 5/8.

Types of Atmospheric Water

Molecules of water vapor in the air are invisible, as are their companion molecules of nitrogen and oxygen. What then are clouds? The somewhat complex answer helps explain the phenomenon of atmospheric precipitation. Most clouds are constituted of tiny drops of liquid water; typically 1 to 100 microns in diameter, while normal fog is simply a water cloud at ground level. Such droplets can cause rainbows, and when seen aloft, a sharp boundary can normally be seen between the water cloud and the surrounding undersaturated air. However, ice clouds are also common, especially at higher altitudes, a familiar type being the feathery cirrus clouds. Ice clouds typically exhibit this indistinct wispy appearance, and it is not possible to delimit them by a sharp boundary. If displaced from the saturated air mass, it appears that tiny ice crystals require more time to disappear by sublimation than cloud droplets require to completely evaporate. In any case, the important point is that different types of condensed H2O can be distinguished, and this provides valuable insight into an important precipitation mechanism.

A key question is, why do cloud droplets and ice crystals not immediately fall from the sky as precipitation? The reason is that they are so tiny that their downward Stokes velocity is small, and slow updrafts are sufficient to keep them aloft. They probably also carry the same electrical charge as their proximal neighbors, repelling each other. Droplets carrying opposite charge appear to be separated by the steep vertical voltage gradient in the atmosphere, thereby creating a giant capacitor within the cloud.

The above considerations provide a basis for explaining the phenomenon of rainfall. Clearly, raindrops and snowflakes are much larger than cloud droplets, fog and ice crystals, so the key problem is how do the droplets coalesce or grow. There are probably several ways to do this, but an important observation is that rain commonly falls from water clouds that have a superjacent “anvil” of ice cloud. It is also well known that many water clouds have temperatures well below the freezing point, and can even be as cold as -20C. The vapor pressure above such supercooled droplets lies along the metastable extension of the equilibrium curve for water-water vapor, and is higher than the vapor pressure of ice (Fig. 4), If ice crystals fall into a supercooled water cloud, the droplets would quickly evaporate as the ice crystals grow, creating large masses that can fall from the sky, commonly melting on the way down, to arrive as raindrops. This mechanism is known as the Begeron process.

Figure 4. Vapor pressure curves for ice and supercooled water, calculated from the equations given in the previous section, agree well with values tabulated by the CRC Handbook of Chemistry and Physics (triangles and dots). Note that the vapor pressure of supercooled water is higher than that for ice at any subzero temperature, indicating that water is unstable relatively to ice under these conditions. Consequently, if ice crystals are introduced into a cloud of supercooled water, the water drops will quickly evaporate while the crystals grow.

Other mechanisms to aggregate cloud droplets have been proposed. Cloud seeding attempts to introduce silver iodide crystals into supercooled clouds, promoting the nucleation of ice which has similar crystal dimensions as the silver iodide. Nuclei of sea salt derived from ocean spray are thought to be effective centers for droplet aggregation, as are certain other aerosols. The author has observed intense downpours shortly after severe thunderclaps, suggesting that lightning changes the charge distribution in clouds in a way that enables the aggregation of droplets that formerly repelled each other.

Precipitation Conditions

Many different atmospheric conditions promote the ascent of air and its attendant adiabatic cooling. This cooling fosters the condensation of water vapor and the subsequent generation of rainfall.

Normal Convection

A common occurrence on a bright summer morning is the formation of small, fluffy cumulous clouds in an otherwise blue sky. As the day progresses and the Sun warms the land, the lower air is heated and rises, causing the clouds to grow. Clouds may become towering thunderheads, 5 to 10 km high, whose upper regions are constituted of ice crystals. Strong storms may feature intense downpours, hail, violent winds, and lightning and thunder. This common mechanism for precipitation is fueled by solar energy, which generates convection cells that drive adiabatic ascent of localized air masses (Fig. 5).

Figure 5. Photo from the International Space Station shows convection cells rising over Indonesia with trailing high altitude ice crystal formations. Convection cell on the right shows the same process as normally observed on the Earth's surface.

Firestorms and Volcanoes

Dark columns of hot smoke or dust rise above large fires or erupting volcanoes. At the top of the column, however, white water clouds can be formed by the forced ascent of air. In extreme cases such as above large forest fires, the condensation of water releases so much latent heat that it invigorates the ascent of the column, and literally “fans the flames” to create dangerous firestorms. Such conditions have killed many firefighters.

Orographic Cooling

In many parts of the world, surface winds are forced to flow over mountain ranges. Orographic clouds commonly form over summits, and though they remain stationary, air rapidly flows through them. Over an annual cycle, precipitation is much higher on the windward side of the mountain than on the leeward side, where the air descends and is adiabatically compressed and heated, which lowers its relative humidity. Such dry areas are termed rain shadows (Fig. 6).

Figure 6. Striking rain shadow in the southwest side of the extinct Kohala volcanic region in northwest Big Island, Hawaii. Prevailing winds from the northeast carry warm moist air up a steep ascent and exhaust cloud precipitation by the crest. Photo NOAA.

Frontal Precipitation

Surface air masses that have different temperatures will have different densities. Such air masses ca be driven by atmospheric circulation pattern, and when they collide, the warmer air must rise over the colder. The interface is called a front, and because it is the locus of air ascent, precipitation commonly occurs along it. Cold fronts occur when a plug of cold air actively impinges on warmer air that commonly contains abundant water vapor. Such fronts are steep and can be associated with violent weather, featuring heavy precipitation, strong winds and rapid temperature changes. Warm fronts are produced when warm air actively impinges on a colder air mass. Such fronts have very low slopes, and light rain or drizzle can occur for protracted intervals. Frontal precipitation is a major cause of continental rainfall and fronts are the most important features on weather maps (Fig. 7).

Monsoons are protracted periods of heavy rainfall, promoted by persistent advection of marine air over continental areas. Best known is the summer monsoon of India. Strong summer heating of the Tibetian highlands produces a huge updraft, causing marine air to flow in, and to cool as it is forced to rise over huge mountains. Heavy rainfall can occur practically every day, for several months.

Global Convergence

As discussed above, persistent global convergence occurs along two belts on Earth, namely in the ITCZ and the Polar Front. Precipitation common forms in the rising air masses above these zones. Because the temperatures of the converging air masses are disparate along the Polar Front but similar along the ITCZ, the resultant storm patterns along the former are much more violent.

Measurements and Data

Precipitation Amount

Precipitation is measured by rain gauges, which typically feature a funnel that collects water into a graduated cylinder of smaller diameter, thereby “magnifying” the water collected, permitting an accurate measurement. The degree of magnification is simply given by the square of the radius ratio of the funnel and the cylinder. The smallest useful funnel diameter is 4” (ca. 10 cm), and is used by the USFS to make measurements of precipitation that can be read to the nearest 0.01 inch (0.25 mm). Snow and ice collected by the device are melted, then reported as “water equivalent”. Of course, evaporation must be prevented.

Snow depths are also important. Various means are used for measurements, including snow stakes in mountain areas. Vertical cylinders of snow are also periodically collected, melted and measured for “water equivalent”, so that future runoff from mountain areas can be predicted.

Reliable data on current rainfall and some long-term records are available for many parts of the world. The data interval, the continuity of the record, and its overall reliability are all important, depending on the needs of the investigator. Annual rainfall amounts, long term averages, seasonal amounts, seasonal averages, daily amounts, hourly amounts, etc. are different quantities with differing applications. For example, the first several of the above would be useless if the effects of a particular storm were of interest, while the detailed storm record would provide no information about climate. Long-term climate change studies depend on the reliability of very old data, which is commonly difficult to ascertain.

Very important data sets for thousands of sites, commonly going back 50 years or more, can be downloaded from NOAA, or otherwise requested. Data collection intervals vary. For many sites, much additional meteorological information is also available.

Water Quality

Normal meteoric precipitation is very dilute, generally less than 10 ppm total dissolved solids, as it basically represents distilled water. Principal ions vary with location, however. Concentrations tend to be highest near the coast, where ordinary salt derived from ocean spray can even be smelled in the air.

A more interesting problem is pH. Water droplets in air should have a slightly acidic pH of 5.6 because atmospheric carbon dioxide dissolves to make weak carbonic acid. Increases in the CO2 content due to fossil fuel combustion have slightly lowered this theoretical value over the last century.

A far more drastic lowering in rainfall pH is caused by sulfate and nitrate aerosols produced by fuel combustion, which interact with water droplets to make sulfuric and nitric acids. The pH of affected rainfall can be well below 4 in areas downwind of coal-fired power plants, and pH was once less than 5 over a huge zone in the eastern USA. The resulting hydrologic and ecological problems were severe, and included dissolution of marble statues and monuments, large zones of dead trees, mobilization of toxic metals into runoff, and acidification of lakes that caused the complete destruction of entire aquatic communities. Most fish cannot live in water with a pH below 5. Fortunately, the severity of these problems has been reduced since ca. 1995 by the installation of air scrubbers and electrostatic precipitators on coal plants, and requiring catalytic converters on cars, but more needs to be done.

Problems

1. The partial pressure of water vapor in a 24oC air body is 12 torr. What is the relative humidity? If the air mass were slowly cooled at constant pressure, at what temperature would water begin to condense? - this is called the “dew point”.

2. Early balloonists knew that air became cooler with elevation, by about 6oC/km. An important scientific question was why temperatures of absolute zero would not be encountered, at heights of only about 45 km! What major scientific discovery was made?

3. Assuming 80% saturation, a surface temperature of 20oC, and a lapse rate of 6oC/km, calculate the amount of “precipitable water” in the troposphere in g/cm2. Assume for this calculation that all of the water vapor is condensed out. Considering your result, what conditions must exist when large amounts of rainfall (>10 cm/day) are delivered?

4. Explain why, in areas of atmospheric contamination, the first rainfall delivered during a light storm can have extremely low pH.